Question

एक आयताकार दरी का क्षेत्रफल 60 मी. है। यदि इस
विकर्ण एवं बड़ी भुजा का योग, छोटी भुजा का 5 गुना हो, :
दरी की लम्बाई होगी​

Answer 1

The length of mat would be 12 meters

Step-by-step explanation:

Consider l be the length and b be the breadth of the mat,

Since, mat is of rectangular shape,

Thus, area of the mat,

$A=lb$

We have,

A = 60 m²,

$lb = 60$                     .........(1),

Diagonal of the rectangle = $\sqrt{l^2+b^2}$

According to the question,

$\sqrt{l^2+b^2}+l = 5b$

$\sqrt{l^2+b^2}= 5b-l$

Squaring both sides,

$l^2 + b^2 = (5b-l)^2$

$l^2 + b^2 = 25b^2 + l^2 - 10lb$

$\implies 24b^2 - 10lb =0$

We have, lb = 60,

$24b^2 - 10(60)=0$

$24b^2 = 600$

$b^2 =\frac{600}{24}$

$b^2 = 25$

$\implies b= 5$    ( Negative value will be neglected because side can not be negative )

$l(5) = 60\implies l =\frac{60}{5}=12$

Hence, the length of the mat would be 12 meters.

#Learn more :

The length of a rectangle is four times its breadth if the the perimeter of the rectangle is 100 cm find it's length and breadth

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Answer 2

Answer:

12

Step-by-step explanation:

Consider l be the length and b be the breadth of the mat,

Since, mat is of rectangular shape,

Thus, area of the mat,

A=lbA=lb

We have,

A = 60 m²,

lb = 60lb=60 .........(1),

Diagonal of the rectangle = \sqrt{l^2+b^2}

l

2

+b

2

According to the question,

\sqrt{l^2+b^2}+l = 5b

l

2

+b

2

+l=5b

\sqrt{l^2+b^2}= 5b-l

l

2

+b

2

=5b−l

Squaring both sides,

l^2 + b^2 = (5b-l)^2l

2

+b

2

=(5b−l)

2

l^2 + b^2 = 25b^2 + l^2 - 10lbl

2

+b

2

=25b

2

+l

2

−10lb

\implies 24b^2 - 10lb =0⟹24b

2

−10lb=0

We have, lb = 60,

24b^2 - 10(60)=024b

2

−10(60)=0

24b^2 = 60024b

2

=600

b^2 =\frac{600}{24}b

2

=

24

600

b^2 = 25b

2

=25

\implies b= 5⟹b=5 ( Negative value will be neglected because side can not be negative )

l(5) = 60\implies l =\frac{60}{5}=12l(5)=60⟹l=

5

60

=12

Hence, the length of the mat would be 12 meters.